Combine first 10 ingredients in processor. Process until well blended, scraping down sides of bowl occasionally.
Arrange chicken in 13 x 9 x 2-inch glass dish. Spoon herb mixture over chicken, covering completely. Cover dish; chill at least 2 hours, turning chicken occasionally. (Can be made 1 day ahead. Keep chilled.)
Meanwhile, prepare barbecue (medium-high heat). Grill chicken until cooked through, about 5 minutes per side.
Cut chicken crosswise into thin slices. Transfer to plates and serve.